A new method for cell volume measurement based on volume exclusion of a fluorescent dye

Several methods currently in use for measuring mean corpuscular volume include: centrifuged packed cell volume, electronic impedance, and light scattering methods. Although these techniques are widely used and accepted, there are problems inherent to each method which may produce systematic errors that are difficult to estimate. This paper describes a new flow cytometric method of cell volume determination, based on the principle of volume exclusion, which may overcome the systematic errors of the methods currently in use. This method requires that the cells be suspended in a fluorescent dye which is unable to penetrate the cell membrane. The level of fluorescence which is produced when a narrow stream of the cell suspension is excited by a focused laser beam will remain constant until a cell arrives in the illuminated region thereby causing a decrease in fluorescence which is directly proportional to the cell's volume. The volume exclusion method is shown to give an estimate of mean red cell volume which correlates well with existing methods.     

Comparison of several digital and stereological methods for estimating surface area and volume of cells studied by confocal microscopy.

BACKGROUND: The implementation of different methods for estimating the surface area and volume of cells studied by confocal microscopy was developed. The methods were compared from the point of view of their precision, applicability and efficiency. METHODS: Interactive stereological methods (spatial grid method, fakir method, Cavalieri principle) as well as automatic digital methods (digital Crofton method, voxel counting, triangulation method, iso-intensity contouring method) were considered. The methods were tested on model geometrical solids and on real volume images consisting of a stack of serial sections encompassing entire tobacco BY-2 cells or cell chains. RESULTS: It is shown that many of the studied methods are very precise when applied to cells of simple or moderately complex shapes. The automatic digital methods are fast and precise but their applicability is limited by the necessity to segment automatically the object surface and to find an optimal resolution. This limitation is not present in stereological methods which are applied interactively and thus are more time-consuming. CONCLUSIONS: The presented implementations of the fakir method and the Cavalieri principle enable interactive, unbiased and efficient estimation of the cell surface area and volume. The recommended steps for measuring the surface area and/or volume of objects studied by confocal microscopy are described.     

MPN estimation of qPCR target sequence recoveries from whole cell calibrator samples

DNA extracts from enumerated target organism cells (calibrator samples) have been used for estimating Enterococcus cell equivalent densities in surface waters by a comparative cycle threshold (Ct) qPCR analysis method. To compare surface water Enterococcus density estimates from different studies by this approach, either a consistent source of calibrator cells must be used or the estimates must account for any differences in target sequence recoveries from different sources of calibrator cells. In this report we describe two methods for estimating target sequence recoveries from whole cell calibrator samples based on qPCR analyses of their serially diluted DNA extracts and most probable number (MPN) calculation. The first method employed a traditional MPN calculation approach. The second method employed a Bayesian hierarchical statistical modeling approach and a Monte Carlo Markov Chain (MCMC) simulation method to account for the uncertainty in these estimates associated with different individual samples of the cell preparations, different dilutions of the DNA extracts and different qPCR analytical runs. The two methods were applied to estimate mean target sequence recoveries per cell from two different lots of a commercially available source of enumerated Enterococcus cell preparations. The mean target sequence recovery estimates (and standard errors) per cell from Lot A and B cell preparations by the Bayesian method were 22.73 (3.4) and 11.76 (2.4), respectively, when the data were adjusted for potential false positive results. Means were similar for the traditional MPN approach which cannot comparably assess uncertainty in the estimates. Cell numbers and estimates of recoverable target sequences in calibrator samples prepared from the two cell sources were also used to estimate cell equivalent and target sequence quantities recovered from surface water samples in a comparative Ct method. Our results illustrate the utility of the Bayesian method in accounting for uncertainty, the high degree of precision attainable by the MPN approach and the need to account for the differences in target sequence recoveries from different calibrator sample cell sources when they are used in the comparative Ct method.     

MPN estimation of qPCR target sequence recoveries from whole cell calibrator samples

DNA extracts from enumerated target organism cells (calibrator samples) have been used for estimating Enterococcus cell equivalent densities in surface waters by a comparative cycle threshold (Ct) qPCR analysis method. To compare surface water Enterococcus density estimates from different studies by this approach, either a consistent source of calibrator cells must be used or the estimates must account for any differences in target sequence recoveries from different sources of calibrator cells. In this report we describe two methods for estimating target sequence recoveries from whole cell calibrator samples based on qPCR analyses of their serially diluted DNA extracts and most probable number (MPN) calculation. The first method employed a traditional MPN calculation approach. The second method employed a Bayesian hierarchical statistical modeling approach and a Monte Carlo Markov Chain (MCMC) simulation method to account for the uncertainty in these estimates associated with different individual samples of the cell preparations, different dilutions of the DNA extracts and different qPCR analytical runs. The two methods were applied to estimate mean target sequence recoveries per cell from two different lots of a commercially available source of enumerated Enterococcus cell preparations. The mean target sequence recovery estimates (and standard errors) per cell from Lot A and B cell preparations by the Bayesian method were 22.73 (3.4) and 11.76 (2.4), respectively, when the data were adjusted for potential false positive results. Means were similar for the traditional MPN approach which cannot comparably assess uncertainty in the estimates. Cell numbers and estimates of recoverable target sequences in calibrator samples prepared from the two cell sources were also used to estimate cell equivalent and target sequence quantities recovered from surface water samples in a comparative Ct method. Our results illustrate the utility of the Bayesian method in accounting for uncertainty, the high degree of precision attainable by the MPN approach and the need to account for the differences in target sequence recoveries from different calibrator sample cell sources when they are used in the comparative Ct method.     

Modeling DNA methylation in a population of cancer cells

Little is known about how human cancers grow because direct observations are impractical. Cancers are clonal populations and the billions of cancer cells present in a visible tumor are progeny of a single transformed cell. Therefore, human cancers can be represented by somatic cell ancestral trees that start from a single transformed cell and end with billions of present day cancer cells. We use a genealogical approach to infer tumor growth from somatic trees, employing haplotype DNA methylation pattern variation, or differences between specific CpG sites or "tags," in the cancer genome. DNA methylation is an epigenetic mark that is copied, with error, during genome replication. At our tags, neutral copy errors in DNA methylation appear to occur at random, and much more frequently than sequence copy errors. To reconstruct a cancer tree, we sample and compare human colorectal genomes within small geographic regions (a cancer fragment), between fragments on the same side of the tumor, and between fragments from opposite tumor halves. The combined information on both physical distance and epigenetic distance informs our model for tumor ancestry. We use approximate Bayesian computation, a simulation-based method, to model tumor growth under a variety of evolutionary scenarios, estimating parameters that fit observed DNA methylation patterns. We conclude that methylation patterns sampled from human cancers are consistent with replication errors and certain simple cancer growth models. The inferred cancer trees are consistent with Gompertzian growth, a well-known cancer growth pattern.     

Interrelations among Na and K content,cell volume,and buoyant density in human red blood cell populations

Summary This study establishes a method for determining the concentration of Na and K in single red blood cells from electron probe microanalysis of a cell's Na and K content. To this end, red blood cells were separated into subpopulations according to their buoyant density by means of bovine serum density gradient centrifugation. Cell water and Na+K contents were then determined in each fraction by conventional analytic methods with cell volume estimated from measurements of hematocrits and cell number. It was found that an inverse relationship obtains between the mean cell volume and buoyant cell density since cells increased in size as density decreased. Although the amount of hemoglobin per cell was found to slightly increase as cell density decreased, hemoglobin concentration showed the inverse relationship, indicating that buoyant cell density differences are primarily the result of differences in hemoglobin concentration. In confirmation of Funder and Wieth (Funder, J., Wieth, J.O. 1966.Scand. J. Lab. Invest. 18:167–180) cell water and cell volume was found to vary directly with the summed content of Na+K. Finally, by means of electron probe microanalysis of single cells, the cellular concentration of hemoglobin was found to vary inversely with the Na+K content, providing a quantitative basis for directly estimating cell volume, and thus ionic concentration, with this technique.     

Bacterial Growth on Surfaces: Automated Image Analysis for Quantification of Growth Rate-Related Parameters

A fast routine method for estimating bacterial cell growth rates by using the metachromatic dye acridine orange is described. The method allows simultaneous estimates of cellular RNA and DNA contents of single cells. Acridine orange staining can be used as a nonspecific supplement to quantitative species-specific hybridizations with fluorescence-labelled ribosomal probes to estimate the single-cell concentration of RNA. By automated analysis of digitized images of stained cells, we determined four independent growth rate-related parameters: cellular RNA and DNA contents, cell volume, and the frequency of dividing cells in a cell population. These parameters were used to compare physiological states of liquid-suspended and surface-growing Pseudomonas putida KT2442 in chemostat cultures. The major finding is that the correlation between substrate availability and cellular growth rate found for the free-living cells was not observed for the surface-bound cells; in contrast, the data indicate an almost constant growth rate for attached cells which was independent of the dilution rate in the chemostat.     

A semicontinuous culture model that links cell growth to extracellular nutrient concentration

During semicontinuous culture, a sample of fixed volume is removed at regular time intervals to make measurements and/or harvest culture components, and an equal volume of fresh medium is immediately added to the culture, thereby instantaneously enhancing nutrient concentrations and diluting cell concentration. The resulting cell concentration versus time curve (i.e., the actual cell growth curve) has a saw-toothed appearance because of the periodic dilution of cell concentration. The observed cell concentrations correspond to the peaks of the saw-toothed curve. Cell growth rates are estimated from the locus of observed cell concentrations (i.e., from the apparent growth curve obtained by connecting the peaks of the saw-toothed curve). The sole preexisting model (Fencl's mode) for estimating cell growth rate is valid only when the cells are growing exponentially at a constant rate between samplings. This model has limited validity: despite the periodic enhancement of nutrient concentration, cell growth between samplings eventually causes nutrient depletion, and the cells cease to grow exponentially. Failure to recognize the limits of validity for Fencl' model has resulted in many erroneous applications of the model and, consequently, many incorrect estimates of cell growth rates. To provide a means for correctly estimating cell growth rates, Fencl's exponential model was extended, and a new model that describes the effects of nutrient depletion on cell growth in semi-continuous culture was obtained. The new model shows that exhaustion of a single growth-limiting nutrient in semicontinuous culture causes the locus of cell concentrations observed at time intervals of Deltat to follow a logistic growth curve. The actual cell growth rate was shown to equal the apparent logistic growth rate plus the effective dilution rate -Deltat(-1) In (1 - f), where f is the ratio of sample volume to total culture volume. Moreover, the model predicts that both the apparent logistic growth rate and the apparent steady-state cell concentration should rise linearly with the concentration of growth-limiting nutrient in the input medium, but fall linearly with increases in the effective dilution rate. The new logistic model for nutrient-limited cell growth in semicontinuous culture was successfully tested using published data for Asterionella formosa, Cyclotella meneghiniana, Daucus carota, and strain L mouse cells.     

Estimating cell lineage from distributions of randomly introduced markers

Cell lineage of a multicellular organism has been analysed by introducing a genetic or chemical marker that is inherited from a cell to its daughter cells and is detectable even after several cell divisions. To construct a complete cell lineage, all the cells at different developmental stages need to be identified, and then the intracellular marker must be introduced to each cell. In this paper, I study a new method of estimating cell lineage based on distributions of intercellular markers observed at a single stage, which are introduced randomly at earlier stages. Assumptions are: (1) cell lineage is invariant between embryos; (2) a small number of cells are marked in each experiment; and (3) the total number of replicate experiments is sufficiently large. Then we identify the most likely cell lineage pattern (or tree topology) as the one that requires the least marker insertions to be compatible with the observed distributions of cell markers. This method is essentially the same as the principle of persimony widely used for ancestral phylogeny reconstruction in evolutionary biology. When the total number of cells is small, we can generate all the possible cell lineages and calculate the minimum number of marker insertions for each candidate, and then choose the cell lineage that requires the least marker insertions. If the number of cells is large, we can use clustering method in which a pair of cells with the highest correlation in marker labelling are merged sequentially. The efficiency of the clustering method in estimating the correct cell lineage is confirmed by computer simulations. Finally, the clustering method is applied to reconstruct the cell lineage of ascidian from experimental data.     

Forest above-ground volume assessments with terrestrial laser scanning: a ground-truth validation experiment in temperate,managed forests

Background and AimsQuantifying the Earth’s forest above-ground biomass (AGB) is indispensable for effective climate action and developing forest policy. Yet, current allometric scaling models (ASMs) to estimate AGB suffer several drawbacks related to model selection and uncertainties about calibration data traceability. Terrestrial laser scanning (TLS) offers a promising non-destructive alternative. Tree volume is reconstructed from TLS point clouds with quantitative structure models (QSMs) and converted to AGB with wood basic density. Earlier studies have found overall TLS-derived forest volume estimates to be accurate, but highlighted problems for reconstructing finer branches. Our objective was to evaluate TLS for estimating tree volumes by comparison with reference volumes and volumes from ASMs.MethodsWe quantified the woody volume of 65 trees in Belgium (from 77 to 2800 L; Pinus sylvestris, Fagus sylvatica, Larix decidua, and Fraxinus excelsior) with QSMs and destructive reference measurements. We tested a volume expansion factor (VEF) approach by multiplying the solid and merchantable volume from QSMs by literature VEF values.Key ResultsStem volume was reliably estimated with TLS. Total volume was overestimated by +21 % using original QSMs, by +9 % and –12 % using two sets of VEF-augmented QSMs, and by –7.3 % using best-available ASMs. The most accurate method differed per site, and the prediction errors for each method varied considerably between sites.ConclusionsVEF-augmented QSMs were only slightly better than original QSMs for estimating tree volume for common species in temperate forests. Despite satisfying estimates with ASMs, the model choice was a large source of uncertainty, and species-specific models did not always exist. Therefore, we advocate for further improving tree volume reconstructions with QSMs, especially for fine branches, instead of collecting more ground-truth data to calibrate VEF and allometric models. Promising developments such as improved co-registration and smarter filtering approaches are ongoing to further constrain volumetric errors in TLS-derived estimates.     

A theory for the estimation of DNA synthesis rates by flow cytometry

A method is presented for estimating the rate of DNA synthesis of a cell population by examining the DNA histogram generated by flow cytometry (FCM). The model is based on the use renewal equations to estimate the steady-state fraction of cells in each DNA compartment. The fraction of cells in each compartment is shown to be related to the Laplace transform of the transit time through that compartment. Two methods are introduced for estimating the rate of DNA synthesis utilizing different transit time distributions. One method is shown to be a simplification of the method of Dean and Anderson. The other method allows for variability in the DNA synthesis rate. The effects of quiescent cells are considered and attention is paid to the various assumptions underlying the estimation.     

A method of estimating the dose to and magnitude of an irradiated area during partial radiation damage based on the results of a cytogenetic analysis of a culture of peripheral blood lymphocytes

The curves, obtained in the in vitro experiments, that show the dependence of the frequency of dicentrics (per a cell with dicentrics) upon dose and percentage of cells with dicentrics are proposed to be used in estimating a dose and body volume affected by partial irradiation (an extreme case of nonuniform exposure) by the analysis of chromosome aberrations in peripheral blood lymphocyte cultures.     

Cell Growth and Division: V. Error Analysis of the Collins-Richmond Equation

Error propagation in the Collins-Richmond equation is analyzed in order to obtain the ratio of the fractional error in rate of cell volume increase to the fractional error in each experimental variable. Typical data are analyzed numerically for the total errors resulting from counting statistics, from spectral broadening, and from volume calibration shift. The measurement of 10⁴ cells can give a precision of better than 10% in the volume growth rate with a volume resolution of 3%.     

Maximum Likelihood Estimation of Genetic Parameters in Cell Populations

In this paper we consider a cell population such as bacteria consisting of two types of cells, mutant and nonmutant. Under the mutation and homogeneous pure birth processes, this paper derives a maximum likelihood estimation procedure for estimating mutation rate and birth rate. The method is applied to Newcombe's data; further some Monte Carlo studies are generated. The numerical results indicate that the method is quite efficient for estimating genetic parameters in cell populations.     

Integrated stereological and biochemical studies on hepatocytic membranes. II. Correction of section thickness effect on volume and surface density estimates

The basic stereological formulas for estimating volume (Vv) and surface (Sv) densities are strictly valid only for true infinitely thin sections; the use of "ultrathin" sections of finite thickness T introduces systematic errors, mostly in the sense of overestimation of the parameters. These errors depend on the size and shape of the structural elements and on T. Correction factors for this effect of T are derived by considering model structures that simulate the shape and arrangement of subcellular organelles: (a) spherical vesicles, (b) disks as models for rough endoplasmic reticulum (RER) cisternae, (c) cylindrical tublules as models for smooth endoplasmic reticulum (SER) tubules, microvilli, etc. For vesicles, a model of discrete convex spherical particles is assumed; the correction factors consider loss of caps due to grazing sections and size distribution of the vesicles. The disk and tubule models are used in connection with the new integral geometric formulas of R.E. Miles which consider random aggregates of "inter-penetrating" particles so that the resultant structure is non- convex and thus approximates in nature the networks characteristic of endoplasmic reticulum (ER). Some practical examples relative to liver cells show that the errors due to section thickness may be of the order of 20-40% or more. Computation formulas as well as graphs are given for the determination of the correction factors for Vv and Sv.     

Robust estimation in pulse fluorometry. A study of the method of moments and least squares.

Most laboratories use least-squares iterative reconvolution (LSIR) as a routine method for estimating decay parameters in pulse fluorometric data. It is shown here, however, that LSIR is very sensitive to small amounts of error in the data whenever two decays become too close to one another, or whenever analyses of three decays are attempted. In such cases, inferior methods of estimating integrals, small zero point shifts, or small errors in the measured exciting light will result in failures of least squares, where the method of moments, with moment index displacement and lambda invariance testing, will succeed. The method of moments is therefore robust with respect to such errors while least squares is not.     

Determination of intracellular osmotic volume and sodium concentration in dunaliella

A new method to measure intracellular volume in Dunaliella was developed, where lithium ions are used as monitors of the extracellular volume. Li⁺ is shown to be impenetrable to the intracellular volume, insignificantly absorbed to the algae, and is rapidly and evenly distributed within the extracellular volume. The method is suggested to be free of several limitations and consistent errors present in several previously employed techniques.

Using the new technique it is shown that both Dunaliella salina and Dunaliella bardawil adjust to a constant cellular volume when grown in a medium containing salt concentrations ranging from 0.5 molar to 4 molar NaCl. That volume is 90 femtoliter per cell for D. salina and 600 femtoliter per cell for D. bardawil. Nonosmotic volume accounts for about 10% of the total cell volume.

The intracellular sodium concentration, as determined with the new technique, was under all experimental conditions tested below 100 millimolar. This was true both for cells grown on 0.5 to 4 molar NaCl, and during the osmoregulatory process. It is thus concluded that intracellular NaCl is a minor contributor to the overall intracellular osmotic pressure in Dunaliella.

     

Curve fitting approach for measurement of cellular osmotic properties by the electrical sensing zone method. II. Membrane water permeability

In a companion paper, we demonstrated that dynamic range limitations can confound measurement of the osmotically inactive volume using electrical sensing zone instruments (e.g., Coulter counters), and presented an improved parameter estimation method in which a lognormal function was fit to the cell volume distribution to allow extrapolation beyond the bounds of the data. Presently, we have investigated the effect of dynamic range limitations on measurement of the cell membrane water permeability (L_p), and adapted the lognormal extrapolation method for estimation of L_p from transient volume data. An alternative strategy (the volume limit adjustment method, in which the measured isotonic volume distribution is used to generate model predictions for curve fitting, and the bounds of the dynamic range are adjusted such that extrapolation is not required) was also developed. The performance of these new algorithms was compared to that of a conventional parameter estimation method. The best-fit L_p values from in vitro experiments with mouse insulinoma (MIN6) cells differed significantly for the different parameter estimation techniques (p < 0.001). Using in silico experiments, the volume limit adjustment method was shown to be the most accurate (relative error 0.4 ± 3.2%), whereas the conventional method underestimated L_p by 19 ± 2% for MIN6 cells. Parametric analysis revealed that the error associated with the conventional method was sensitive to the dynamic range and the width of the volume distribution. Our initial implementation of the lognormal extrapolation method also yielded significant errors, whereas accuracy of this algorithm improved after including a normalization scheme.     

Kinetics of water loss from cells at subzero centigrade temperatures

A mathematical model is developed for the calculation of the kinetics of water loss from cells at subzero centigrade temperatures. In this model it is assumed that the cell surface membrane is permeable to water only, the protoplasm is a nonideal solution, the cells are spherical, and during the cooling process the cell temperature is not uniform inside the cell. It is also assumed that because of water loss due to cooling process the cell volume and the cell surface area reduce and the reductions in surface area and volume of the cell are functions of the amount of water loss from the cell. Based on this model, and for different conditions, the fractions of supercooled intracellular water remaining in the cells at various temperatures are calculated.It is shown that for cooling cells at subzero centigrade temperatures. (1) the consideration of Clausius-Clapeyron equation for vapor pressures of water and ice, instead of the exact vapor pressure relations, may produce errors in the prediction of the amount of water loss from the cells at high cooling rates only, (2) the assumption of intact cells will produce considerable deviation in the prediction of water loss from the cells as compared to the more realistic assumption of shrinkable cells, (3) the nonideality of protoplasm solution is very effective on the prediction of the amount of water loss from the cells, and (4) the assumption of uniform-temperature cells during the cooling process may be erroneous only for cells with small fractions of water in their protoplasms.     

Curve fitting approach for measurement of cellular osmotic properties by the electrical sensing zone method. I. Osmotically inactive volume

We have investigated the confounding effects of dynamic range limitations on measurement of the osmotically inactive volume using electrical sensing zone instruments (e.g., Coulter counters), and propose an improved approach to parameter estimation. The conventional approach for analysis of cell size distributions measured by such particle sizing instruments requires data truncation: the mean cell volume is computed after exclusion of data below a specified lower bound (typically chosen to remove artifacts due to small-volume noise) and above an upper bound (typically governed by instrument limitations). The osmotically inactive volume is then estimated from a Boyle–van’t Hoff plot of the averaged volume data obtained after exposure to various solution osmolalities. We demonstrate that systematic exclusion of data in the conventional approach introduces bias that results in erroneously high estimates of the osmotically inactive volume fraction. To minimize this source of error, we have devised a new algorithm based on fitting a bimodal distribution model to the non-truncated volume data. In experiments with mouse insulinoma (MIN6) cells, the osmotically inactive volume fraction was estimated to be 0.15 ± 0.01 using the new method, which was significantly smaller than the estimate of 0.37 ± 0.02 obtained using the conventional method (p < 0.05). In silico experiments indicated that the parameter estimate obtained by the new method was accurate within 5%, whereas the error associated with the conventional approach was approximately 150%. Parametric analysis was used to elucidate the sensitivity of errors to variations in instrument dynamic range and cell volume distribution width.